This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 3 Matrices – Quiz 3 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 3 Matrices Quiz 3 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. If x + 5 is the mean proportional between x + 2 and x + 9; find the value of x. A) 5. B) 6. C) 7. D) 4. Show Answer Correct Answer: C) 7. 2. If A and B are two square matrices such that AB = BA = I, then B is theinverse matrix of A and is denoted by A-1 but A is not the inverse of B. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 3. Solve the system for the value of x. 5x + 8y =-123x + 5y =-7 A) -1. B) -4. C) 1. D) No solution. Show Answer Correct Answer: B) -4. 4. Matriz que busca el ser y la esencia del ser humano es A) Ninguna. B) Ortogonal. C) Horizontal. D) Vertical. Show Answer Correct Answer: B) Ortogonal. 5. If A is singular matrix, then A (adj A) = A) A unit matrix. B) A null matrix. C) A symmetric matrix. D) None of these. Show Answer Correct Answer: B) A null matrix. 6. A classroom has a seating arrangement where the number of rows is equal to the number of columns. In this scenario, when is the classroom considered to have a square seating arrangement? A) The number of rows is equal to the number of columns. B) The number of rows is greater than the number of columns. C) The number of rows is less than the number of columns. D) None of these. Show Answer Correct Answer: A) The number of rows is equal to the number of columns. 7. The rank of Null matrix is ..... A) 1. B) 0. C) 3. D) 2. Show Answer Correct Answer: B) 0. 8. Cayley-Hamilton's theorem is A) The product of the characteristic roots of a square matrix of order n is equal to the determinant of the matrix. B) Every square matrix satisfies its own characteristic equation. C) For a square matrix A. $\lambda$ is a characteristic root iff there exists a nonzero vector X such that AX=$\lambda$X. D) The characteristic roots of a real symmetric matrix are all real. Show Answer Correct Answer: B) Every square matrix satisfies its own characteristic equation. 9. How many COLUMN and RAW are there in a Matrix of order $2\times3$ A) 2 and 3. B) 3 and 3. C) 3 and 2. D) None of these. Show Answer Correct Answer: C) 3 and 2. 10. If A is a singular matrix, then A adj (A) is a/an a. scalar matrix b. zero matrix c. identity matrix d. orthogonal matrix A) B. B) D. C) A. D) C. Show Answer Correct Answer: A) B. 11. Derivative of tan 7x w.r.t. x = A) (tan 7x)/7. B) (Sec$^{2}$ 7x)/7. C) 7 Sec$^{2}$7x. D) 7 tan 7x. Show Answer Correct Answer: C) 7 Sec$^{2}$7x. 12. What is the determinant of the matrix | 2 3 | | 5 7 |? A) -1. B) 1. C) 4. D) -4. Show Answer Correct Answer: D) -4. 13. The number of columns in a 2x12 matrix is? A) 2. B) 10. C) 24. D) 12. Show Answer Correct Answer: D) 12. 14. Find two numbers such that the mean mean proportional between them is 12 and the third proportional to them is 96. A) 6 and 12. B) 3 and 18. C) 6 and 24. D) 3 and 30. Show Answer Correct Answer: C) 6 and 24. 15. If the number of elements of a matrix represents a prime Number (p), then the number of matrices possible is A) 1. B) P. C) 2. D) None of these. Show Answer Correct Answer: C) 2. 16. A-B = A + (-1) B this property of matrices is not correct A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 17. If |A| = 0, then A is A) Non-singular matrix. B) Singular matrix. C) Identity matrix. D) Zero matrix. Show Answer Correct Answer: B) Singular matrix. 18. When solving a system AX=B using inverse matrices, you use the equation: A) X=B$^{-1}$A. B) A=X$^{-1}$B. C) B=X$^{-1}$A. D) X=A$^{-1}$B. Show Answer Correct Answer: D) X=A$^{-1}$B. 19. What is the order of the matrix [[1, 2, 3], [4, 5, 6]]? A) 2 x 3. B) 2 x 2. C) 3 x 2. D) 1 x 3. Show Answer Correct Answer: A) 2 x 3. 20. What is the definition of scalar multiplication of matrices? A) Scalar multiplication of matrices is the process of multiplying each element of a matrix by a scalar (a single number). B) Scalar multiplication is the process of dividing each element of a matrix by a scalar. C) Scalar multiplication is the process of finding the determinant of a matrix. D) Scalar multiplication is the process of adding two matrices together. Show Answer Correct Answer: A) Scalar multiplication of matrices is the process of multiplying each element of a matrix by a scalar (a single number). 21. What is the result of multiplying matrices M = [[3, 4, 2], [1, 5, 0]] and N = [[13, 9], [8, 7], [6, 4]]? A) [[74, 55], [46, 35]]. B) [[83, 63], [53, 42]]. C) [[76, 58], [40, 35]]. D) [[92, 73], [46, 35]]. Show Answer Correct Answer: B) [[83, 63], [53, 42]]. 22. If A and B are symmetric matrices, then ABA is a A) Diagonal matrix. B) Symmetric matrix. C) Scalar matrix. D) Skew-symmetric matrix. Show Answer Correct Answer: B) Symmetric matrix. 23. What is the condition for two matrices to get added? A) They must be square. B) There order must be equal. C) The determinant can't equal 0. D) None of these. Show Answer Correct Answer: B) There order must be equal. 24. Los establecimientos de comercio abiertos para una sociedad en el interior o el exterior, dirigidos por administradores con facultades para representar la sociedad central, se denominan: A) Subsidiarias. B) Sucursales. C) Filiales. D) Agencias. Show Answer Correct Answer: B) Sucursales. 25. Using determinants, find the area of the triangle whose vertices are (0, 0), (4, 3) and (8, 0). A) 12. B) 21. C) 24. D) NONE OF THE ABOVE. Show Answer Correct Answer: A) 12. 26. Si la matriz A es de orden 2 x 4 y la B es de 4x 3, el producto de A.B es de orden: A) 4x4. B) 3x2. C) 2x2. D) 2x3. Show Answer Correct Answer: D) 2x3. 27. If [4 8] = [2+2 12-4], the it is a/an: A) Rectangular matrix. B) Equal matrix. C) Singular matrix. D) Square matrix. Show Answer Correct Answer: B) Equal matrix. 28. The value of a ..... does not change when rows and columns are interchanged. A) Matrix. B) Determinant. C) Linear space. D) None of the above. Show Answer Correct Answer: B) Determinant. 29. If A be any square matrix, then AA' and A'A will be both A) Either skew symmetric or symmetric. B) Neither skew symmetric nor symmetric. C) Skew symmetric. D) Symmetric. Show Answer Correct Answer: D) Symmetric. 30. If all the elements of a matrix are zeros, it is: A) Equal matrix. B) Null matrix. C) Square matrix. D) Rectangular matrix. Show Answer Correct Answer: B) Null matrix. 31. Matrices are usually named using A) A number. B) Two numbers. C) A letter. D) A capital letter. Show Answer Correct Answer: D) A capital letter. 32. If a square matrix A is symmetric matrix then kA is (where k is some scalar) A) Symmetric if k is negative. B) A symmetric matrix. C) A skew symmetric matrix. D) Symmetric matrix if k is positive. Show Answer Correct Answer: B) A symmetric matrix. 33. (2 x 3) Matrix have A) 2 Rows and 3 Columns. B) 3 Rows and 2 Columns. C) 6 Rows and 6 Columns. D) None of the above. Show Answer Correct Answer: A) 2 Rows and 3 Columns. 34. A matrix which diagonal elements are equal and non-diagonal elements are zero is called A) ROW MATRIX. B) COLUMN MATRIX. C) DIAGONAL MATRIX. D) SCALAR MATRIX. Show Answer Correct Answer: D) SCALAR MATRIX. 35. |A| not= 0, name the matrix A) Non-singular. B) Singular. C) Diagonal. D) Square. Show Answer Correct Answer: A) Non-singular. 36. Si el determinante de una matriz es cero entonces: A) La matriz tiene inversa. B) La matriz no tiene inversa. C) La matriz tiene adjunta. D) La matriz no tiene adjunta. Show Answer Correct Answer: B) La matriz no tiene inversa. 37. What is matrix addition? A) Subtracting the corresponding elements of two matrices. B) Multiplying the corresponding elements of two matrices together. C) Dividing the corresponding elements of two matrices. D) Adding the corresponding elements of two matrices together. Show Answer Correct Answer: D) Adding the corresponding elements of two matrices together. 38. Matrix multiplication is associative. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 39. Solution of the system defined by the set of equations 4y+ 3z = 8, 3x-z = 2 and 3x+ 2y = 5 is A) Does not exist. B) X=0, y=1/2, z=2. C) X=1, y=1/2, z=2. D) X=0, y=1, z=4/3. Show Answer Correct Answer: A) Does not exist. 40. 5). If A is any square matrix, then A) A+A$^{t}$ is symmetric. B) A-A$^{t}$ is symmetric. C) A+A$^{t}$ is skew-symmetric. D) None of these. Show Answer Correct Answer: A) A+A$^{t}$ is symmetric. 41. State True or false:Matrix addition is associative as well as commutative. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 42. If A is a square matrix Ax=$\lambda$x for nonzero scalar $\lambda$, then x is an eigenvector of A A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 43. Let A be a square matrix of order 3x3 then| kA| = . A) K$^{2}$|A|. B) K$^{3}$|A|. C) K |A|. D) 3k|A|. Show Answer Correct Answer: B) K$^{3}$|A|. 44. Solve by elimination. $4x-4y=-20$ $10x-5y=10$ A) ( 12, 7). B) ( 4, -1). C) (-1, 4). D) (7, 12). Show Answer Correct Answer: D) (7, 12). 45. You can multiply a 2X3 matrix by a matrix of order A) 2X12. B) 2X2. C) 3X12. D) 2X3. Show Answer Correct Answer: C) 3X12. 46. If the product of two real number is one then number are called: A) Null matrices. B) Additive inverse of each other. C) Equal matrices. D) Multiplicative inverse of each other. Show Answer Correct Answer: D) Multiplicative inverse of each other. 47. Matrix addition is associative. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 48. *If A is a square matrix of order 3 such that |adj. A|=16. then what will be |A| A) 4. B) 13. C) -16. D) 16. Show Answer Correct Answer: A) 4. 49. If A and B are invertible matrix then (AB)$^{-1}$ = A) A$^{-1}$B$^{-1}$. B) AB. C) B$^{-1}$A$^{-1}$. D) None of these. Show Answer Correct Answer: C) B$^{-1}$A$^{-1}$. 50. Let D be a non-zero n x n real matrix with n$\geq$2 which of the following implications is valid? A) Rank(D) = n $\Longrightarrow$ $\ne$. B) A) det(D) = 1 $\Longrightarrow$ $\ne$. C) Det(D) = 0 $\Longrightarrow$. D) Rank(D) =1 $\Longrightarrow$ $\ne$. Show Answer Correct Answer: B) A) det(D) = 1 $\Longrightarrow$ $\ne$. 51. How is the cofactor of an element aij defined? A) Aij = (-1)ijMij, where Mij is the square of the element aij. B) Aij = (-1)ijMij, where Mij is the product of the elements in the ith row and jth column. C) Aij = (-1)ijMij, where Mij is the determinant obtained by deleting the ith row and jth column. D) Aij = (-1)ijMij, where Mij is the sum of the elements in the ith row and jth column. Show Answer Correct Answer: C) Aij = (-1)ijMij, where Mij is the determinant obtained by deleting the ith row and jth column. 52. Para obtener la inversa de una matriz se tiene que A) Cambiar las filas por las columnas. B) Cambiar el signo de los elementos de la matriz. C) Las dos anteriores. D) Ninguna. Show Answer Correct Answer: B) Cambiar el signo de los elementos de la matriz. 53. The number of all possible matrices of order $2\times3$ A) 24. B) 6. C) 64. D) 16. Show Answer Correct Answer: C) 64. 54. A non homogeneous system of linear equations may have A) Zero solution only. B) Non zero solution only. C) Zero solution and/or non zero solution. D) None. Show Answer Correct Answer: C) Zero solution and/or non zero solution. 55. Calculate the difference between the matrices C = [[5, 6], [7, 8]] and D = [[3, 2], [1, 4]]. A) [[6, 5], [4, 3]]. B) [[1, 2], [3, 4]]. C) [[4, 3], [2, 1]]. D) [[2, 4], [6, 4]]. Show Answer Correct Answer: D) [[2, 4], [6, 4]]. 56. Solve for x:x-y =-6x + y = 8 A) 1. B) -1. C) 8. D) 7. Show Answer Correct Answer: A) 1. 57. Let AX=B be a system of m linear equations in n variables.If |A|=0 and adj(A).B=0, then the system is ..... A) Consistent and has unique solution. B) Consistent and has infinite number of solutions. C) Inconsistent and has no solution. D) None of the above. Show Answer Correct Answer: B) Consistent and has infinite number of solutions. 58. If B is the inverse of A, then A is also the inverse of B. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 59. The equation C = 50 + 1.25 (x-100) models the yearly cost, C, to use a professional photo printing service. To use the service, Jessica pays a $ 50 yearly subscription fee and $ 1.25 per photo after the first 100 photos (the first 100 photos are included with the $ 50 subscription). The variable x represents the number of photographs. Rewrite the formula for x in terms of C. A) $x=C+40$. B) $x=\frac{c}{1.25}+\frac{50}{1.25}$. C) $x=.8c+40$. D) $x=.8c+60$. Show Answer Correct Answer: D) $x=.8c+60$. 60. En una matriz identidad de orden 4, los elementos suman ..... A) 6. B) 2. C) 8. D) 4. Show Answer Correct Answer: D) 4. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 3 Matrices Quiz 1Class 12 Mathematics Chapter 3 Matrices Quiz 2Class 12 Mathematics Chapter 3 Matrices Quiz 4Class 12 Mathematics Chapter 3 Matrices Quiz 5Class 12 Mathematics Chapter 3 Matrices Quiz 6Class 12 Mathematics Chapter 3 Matrices Quiz 7Class 12 Mathematics Chapter 1 Relations And Functions QuizClass 12 Mathematics Chapter 10 Vector Algebra Quiz 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books